Concept
♦
Activity 11
Why Aren’t There More
Reds in My Bag?
Statistics
Skills
♦
Finding ratios
♦
Creating circle graphs
♦
Sampling data
♦
Understanding sample size
♦
Calculator skills: t, 3, category lists, v
Materials
Students will use small bags of M&M’sê to make
predictions, gather data, and display color
distribution results in a circle graph.
♦
Student Activity sheets (page 58)
♦
TI-73 calculators
♦
Small bags of Plain M&M’sê (47.9g or 21g)
♦
Transparency of circle graph showing actual
distribution of colors (page 60)
♦
Manila paper
Activity
Warning: M&M’sê, even the plain ones, contain peanut oil. Before doing
this activity, check to see if anyone in your class has a peanut allergy. If they
do, you may want to use another candy similar to M&M’sê.
Distribute the bags of M&M’sê to each student with instructions not to open
or eat them.
Ask questions about the bags of M&M’sê:
♦ How many M&M’sê do you think are in each bag?
♦ How many colors do you think are in each bag?
♦ How many of each color? Record your predictions on the Student Activity sheet.
♦ Do you think that each bag has the same colors? Same quantity of
M&M’sê? Same quantity of each color? Why or why not?
Have students open the bags and sort the M&M’sê by color, again with
instructions not to eat.
Tell each student to record the number of each color on the Student Activity
sheet. Then have them record each color as a ratio, decimal, and percent of
the total number of M&M’sê in their bag. Discuss the concept of ratio and
percent if needed.
© 1998 TEXAS INSTRUMENTS INCORPORATED
54
Discovering Mathematics with the TI-73: Activities for Grades 5 and 6
Have each student compare the number of M&M’sê in his or her bag to those
of another student.
Ask students these questions:
♦ Do you and your partner have the same number of each color of M&Ms ê?
♦ Does your partner have the same total number of M&M’sê?
♦ Are all colors represented in both bags?
Have students arrange the colors of M&M’sê in a circle on manila paper,
with like colors together and the sides of the M&M’sê touching. Trace around
the circle. Estimate the center and mark it. Draw a line from the center to
the point where the color changes on the circle. Label each section with the
color, the ratio to total M&M’sê, and percent.
Green
10%
Orange
10%
Red
20%
Brown
30%
Yellow
20%
Blue
10%
Create a list on the TI-73 called COLOR.
1.
Press 3.
2.
Press " to move to the right of L6 to the
first unused list.
3.
To name the list COLOR, press - t
and use the arrow keys to spell COLOR,
pressing b after each letter.
4.
When finished, press # to move down to
Done and press b.
© 1998 TEXAS INSTRUMENTS INCORPORATED
Activity 11: Why Aren’t There More Reds in My Bag?
5.
Press b again and the list will be
named.
6.
Press # to get COLOR(1)=
7.
Enter the colors of the M&M’sê into the
list.
55
Be sure to make the list a category list.
To do this, enclose the first element in
quotation marks (found in the text editor)
when you enter it.
8.
Press - t and use the arrow keys to
spell BROWN, pressing b after each
letter.
9.
Press # to move to Done and press b.
10. Press b again and BROWN will be
pasted on the calculator screen under
COLOR.
11. Continue this process until you have
entered all the colors.
Note: You only have to use the quotation marks for the
first color entered.
Now you are ready to enter the data.
1.
Using the arrow keys, move to the top of
list 8 and create a list called DATA using
the text editor just as before.
2.
When finished, press # to get to the first
element in the list.
3.
Enter the number of each color in this
list, pressing b after each number.
Tip: This is not a categorical list, so no quotes are needed for the first element.
© 1998 TEXAS INSTRUMENTS INCORPORATED
56
Discovering Mathematics with the TI-73: Activities for Grades 5 and 6
Create a circle graph from the data.
Note: You do not need to set window values for a circle
graph.
1.
On the calculator, press - e.
2.
Select 1:Plot1 and press b.
3.
Press b to highlight ON.
4.
Press # and " to move to the circle graph and press b to select it.
5.
For CategList, you want the list you named COLOR. To get this list, press
- v, use the arrows to move down to COLOR, and press b.
6.
Follow the same procedure for the Data List, but choose the list you
named DATA.
Before graphing, make sure all other plots are turned off.
1.
Press - e.
2.
If a plot other than Plot 1 is turned on, use the arrow keys to highlight
that plot and press b.
3.
Use the arrow keys to highlight Off and press b to turn it off.
4.
Press * to see the circle graph.
5.
Press ) and use the arrow keys to explore the circle graph with
students.
Have the students sketch the circle graph on the Student Activity sheet. Be
sure that they label the colors and percents.
Ask the students:
♦ Compare this graph with the one you created with your M&M’sê. What do
you notice?
Combine data with three other classmates by adding the data together and
entering it into a new list called Group. Create a new circle graph by pressing
- v and selecting 2:PLOT 2.
Tip: You cannot display two circle graphs at the same time. You must first turn off Plot 1 and
then set this list up as Plot 2.
Sketch and compare this circle graph with the circle graph for your own data.
Be sure to label the circle graph.
Repeat the process by combining the whole class data into another list called
class. Set this graph up as Plot 3. (Remember to turn off Plots 1 and 2.)
Sketch and compare this circle graph with the two previous graphs.
Ask the students:
♦ How do these three circle graphs compare?
♦ How are they different? Why?
© 1998 TEXAS INSTRUMENTS INCORPORATED
Activity 11: Why Aren’t There More Reds in My Bag?
57
Wrap-Up
Compare the three circle graphs to the circle graph supplied (page 60)
showing the actual distribution of colors in a package of plain M&M’sê.
♦ How are the three circle graphs the same?
♦ How are they different?
♦ Which of your charts is closest to the one showing the actual distribution?
♦ Why?
Note: At this point you should discuss the idea of a small quantity of data (individual) versus
a larger quantity of data (class).
♦ Why wouldn’t all bags of M&M’sê be the same?
♦ How do you think they chose the colors for M&M’sê that they use?
♦ How did they choose how many of each color to include?
Assessment
Have the students write about why the graphs might be different from
others.
Collect the sketches of the circle graphs.
Make a circle graph with different data and give it to students with questions
to answer.
Extensions
♦ Do the same experiment using a different candy.
♦ Compare the difference between the color distribution in plain M&M’sê
bags and peanut M&M’sê bags. Is there a difference?
© 1998 TEXAS INSTRUMENTS INCORPORATED
Student Activity
Name
_________________________
Date
_________________________
Activity 11
Why Aren’t There More Reds?
Record your predictions in the table below, then open the bags and record the actual
number of each color. Determine the ratio, decimal amount, and the percentage of the
total number in the bag that each color represents.
Color
Prediction
Actual
Ratio to
Total
Brown
Green
Yellow
Red
Orange
Blue
Circle Graph of my data
© 1998 TEXAS INSTRUMENTS INCORPORATED
Decimal
Percent
Activity 11: Why Aren’t There More Reds in My Bag?
59
Circle Graph of my group’s combined data
Circle Graph of the class data
© 1998 TEXAS INSTRUMENTS INCORPORATED
60
Discovering Mathematics with the TI-73: Activities for Grades 5 and 6
Actual Distribution of Colors
Green
10%
Orange
10%
Red
20%
Brown
30%
Yellow
20%
Blue
10%
TRANSPARENCY MASTER
© 1998 TEXAS INSTRUMENTS INCORPORATED